Students who choose this option will complete an M2 (second year) master program in introduction to modelling methodology, as well as interdisciplinary courses and applications of complex networks. An internship is also included in the second semester. The purpose of this program is to provide to students an extensive view on tools for modeling complex systems, and to provide courses with an interdisciplinary approach to single subjects.

For more complete information about this option, visit the IXXI website at www.ixxi.fr/M2.php

Courses assigned for Computer Science students

The course provides an introduction to complex network theory by walking through the established methods and the most recent techniques of modeling and analyzing structured complex systems. During the course we will define the general properties and measures of complex networks, fundamental network models (ER networks, SW networks, BA networks), structural phase-transitions, bipartite networks, node and link centrality measures, network modularity and community detection methods, temporal and evolving networks.

This lecture will cover modern techniques in signal processing for data which are distributed over networks. Analysis of data over networks or graphs (also called graph signals) is currently a very active domain, and we will study approaches combining signal and image processing, graph theory (especially algebraic methods such as spectral analysis of graphs), and distributed methods on networks. The application of signal processing for networks range from the study of technological networks (of sensors, in telecommunication or transport) to more general complex networks such as biological or social networks. Three main topics will be covered. Fist, harmonic analysis on graphs will be discussed, going from simple Fourier transform suited to graph signals to multi-scale wavelet analysis. Second, variational approaches on graphs will be discussed, allowing to methods such as denoising, restoring, inference or clustering on graphs. For that, modern optimization approaches based on monotone operators will also be introduced. Finally, the distributed methods will be considered, especially for distributed consensus, estimation or detection in a network, including methods using distributed optimization.

Dealing with large (real life) graphs leads to several problems among which one can highlight two major questions: How to generate them? and How to make computations on them? These two directions have a common feature in the sense that one cannot access the full graph, but only parts of it. This refines our approach into : How to generate a graph under some constraints (usually local ones like degree, density of triangles, etc)? and How to compute properties of the graph under statistical knowledge? These question are far reaching, and the objective of this course is to introduce some (usually probabilistic) tools to this purpose.